Question: $\dfrac{ -2b + 5c }{ -3 } = \dfrac{ 5b - 6d }{ 4 }$ Solve for $b$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -2b + 5c }{ -{3} } = \dfrac{ 5b - 6d }{ 4 }$ $-{3} \cdot \dfrac{ -2b + 5c }{ -{3} } = -{3} \cdot \dfrac{ 5b - 6d }{ 4 }$ $-2b + 5c = -{3} \cdot \dfrac { 5b - 6d }{ 4 }$ Multiply both sides by the right denominator. $-2b + 5c = -3 \cdot \dfrac{ 5b - 6d }{ {4} }$ ${4} \cdot \left( -2b + 5c \right) = {4} \cdot -3 \cdot \dfrac{ 5b - 6d }{ {4} }$ ${4} \cdot \left( -2b + 5c \right) = -3 \cdot \left( 5b - 6d \right)$ Distribute both sides ${4} \cdot \left( -2b + 5c \right) = -{3} \cdot \left( 5b - 6d \right)$ $-{8}b + {20}c = -{15}b + {18}d$ Combine $b$ terms on the left. $-{8b} + 20c = -{15b} + 18d$ ${7b} + 20c = 18d$ Move the $c$ term to the right. $7b + {20c} = 18d$ $7b = 18d - {20c}$ Isolate $b$ by dividing both sides by its coefficient. ${7}b = 18d - 20c$ $b = \dfrac{ 18d - 20c }{ {7} }$